If you have a small empire, diplomacy is critical. If a leading AI is allowed to peacefully tech and develop while you sit there with 4 cities, you'll lose. If an AI is allowed to overrun his neighbors one-by-one, you'll lose. And if you get seriously attacked any time after the Medieval period, you'll lose. So you need to be bribing to start wars, sharing religions and civics, giving in to demands, accurately judging which AIs are the threats...
This can buy you a fair amount of time, but even best-case AIs are going to start out-teching you around the end of the Medieval. Eventually you may have very few options for bribing AIs to start wars, so it's important that you get all the diplomatic blocs balanced nicely and thoroughly hating each other as quickly as possible.
Even if everything breaks your way, odds are you won't be able to get a spaceship victory without going down a level or two from where you normally play. UN victory will be unusually tough. But cultural and AP will be quite possible, if you plan for them from the start. Because the other feature of this sort of small empire is that you have no wiggle room to adjust plans when things go wrong.
yatta (he posted above) played some Immortal Minimalism games recently that were a great demonstration of how much can be achieved by simply setting an early plan and sticking to it.